Subject: Query on closed homology
Date: Tue, 9 Oct 2001 12:20:33 -0400
From: Allen Hatcher <hatcher@polygon.math.cornell.edu>
To: Don Davis <dmd1@lehigh.edu>

Question for the algebraic topology discussion list:

Some papers of Kontsevich mention a kind of homology called "closed
homology" or "homology with closed supports." Can anyone clarify for
me what this terminology means, or give a reference to the literature
for a definition? Presumably it's just a different name for something
familiar. From context I'm guessing that it is homology with infinite
but locally finite chains. For example, for a locally finite
simplicial complex this would be equivalent to homology using
infinite simplicial chains. For spaces that are sufficiently nice at
infinity it would be equivalent to the reduced homology of the
one-point compactification.

(A colleague asked me this question, and I want to make sure I gave
the right answer.)

Allen Hatcher